Mechanical coolant pumps of the prior art are described in WO 2004 059142 A1. These pumps comprise a pump rotor wheel and a housing which supports numerous variable pump stator blades. The pump is assembled by first mounting the variable pump stator blades in respective pivot openings in the housing. After the pump rotor wheel has been mounted, the pump is transferred to a combustion engine block to be installed at the engine block. During the transfer, the stator blades are not secured against loosening so that they can drop out.